This application claims the benefit of a Japanese Patent Application No.2002-176016 filed Jun. 17, 2002, in the Japanese Patent Office, the disclosure of which is hereby incorporated by reference.
1. Field of the Invention
The present invention generally relates to simulation methods, simulation apparatuses and computer-readable storage media, and more particularly to a simulation method and a simulation apparatus which are suited for making a noise analysis by simulation when designing electronic circuits such as large scale integrated circuits (LSIs), multi chip modules (MCMs) and printed circuit boards (PCBs), and to a computer-readable storage medium which stores a program for causing a computer to carry out such a simulation.
Recently, due to reduce size and increased operation speed of various electronic circuits, it has become important to make a noise analysis and to take noise countermeasures when designing an electronic circuit. The noise countermeasures refer to various measures which are taken in order to suppress noise generated in the electronic circuit, based on results of the noise analysis.
2. Description of the Related Art
Conventionally, various noise analyzing tools have been proposed to make the noise analysis when designing the electronic circuit. The noise analyzing tool makes the noise analysis and a noise check using a circuit simulator after making the assemble design of the electronic circuit, so as to determine the noise countermeasures for suppressing the noise. The design of the electronic circuit is modified based on the determined noise countermeasures if necessary. After the design modification, a noise analysis and a noise check are made again, and the above described procedure is repeated until the noise falls within a tolerable range.
The noise to be mainly considered when designing the electronic circuit includes reflection noise and crosstalk noise. Normally, the reflection noise is generated due to a mismatch between characteristic impedances of an internal resistance of a driver and a transmission line. On the other hand, the crosstalk noise greatly depends on a driving capability of the driver and a gap (pitch) of an adjacent wiring pattern.
When making the noise analysis using a circuit simulator, the noise analysis is made based on various parameters, and the various parameters include a skin resistance coefficient which takes into consideration the skin effect. The skin effect refers to a phenomenon where the resistance increases towards a central portion of a conductor forming the wiring, and a current only flows in a vicinity of the conductor surface. The skin resistance coefficient refers to a resistance coefficient of the conductor which takes into consideration the skin effect. The effects of the skin effect no longer becomes negligible as the frequency of the signal passing through the conductor becomes high. Generally, the resistance of the conductor changes depending on the signal frequency, but if the skin resistance coefficient is known, the resistance of the conductor can be described as a function of the signal frequency, thereby making it possible to make a simulation with respect to an arbitrary signal frequency. For example, the resistance of the conductor and the skin resistance coefficient may be calculated based on an algorithm described in W. T. Weeks et al., “Resistive and Inductive Skin Effect in Rectangular Conductors”, IBM J. RES. DEVELOP. Vol.23, No.6, pp.652-660, November 1979.
Conventionally, there exists a noise analyzing tool which divides the conductor into a plurality of parts when calculating the resistance of the conductor by taking into consideration the skin effect. However, in order to obtain the resistance of the conductor with a high accuracy, it becomes necessary to divide the conductor into a large number of small parts, and a calculation time is increased thereby. Particularly when making the noise analysis of a plurality of conductors such as adjacent wirings, the width of the ground becomes larger as the pitch of the conductors becomes larger, and it takes an extremely long time to make the calculations when the resistance of the conductor is calculated by dividing the conductor into a large number of small parts.
According to the conventional noise analyzing tool, the resistance of the conductor is calculated by taking into consideration the skin effect, regardless of a magnitude of the pitch of the conductors. For this reason, when calculating the resistance of the conductor by dividing the conductor into a large number of small parts, there were problems in that it takes an extremely long time to make the calculations, and that the noise analysis cannot be made at a high speed.